The talk concerns with several recent results in the theory of harmonic measure: the one, two and three phase problem for harmonic measure. These problems were formulated by Chris Bishop in the early 90's. Along with interesting potential theory ingredients their solutions are based on recent achievements of a non-homogeneous theory of Calder\on--Zygmund operators, on a non-homogeneous T1 theorem, and on a solution of David--Semmes problem that asked to relate the boundedness of singular Riesz transform operator with the wrectifiability of the underlying surface measure.